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Fitzhugh-Nagumo equations in a nonhomogeneous medium. (English) Zbl 1162.35393
Summary: We investigate various propagation phenomena for the FitzHugh-Nagumo system
\[ \begin{cases} u_t = Du_{xx}+u(1-u)(u-a(x))-v,\\ v_t = \varepsilon(gu-bv-d),\\ u(x,0)=u_0(x),\\ v(x,0)=v_0(x),\\ u_x(0,t)=u_x(L_t)=0.\end{cases} \]
with a nonhomogeneous threshold function \(a(x)\). It is studied over a range of values \(b\), \(d\), \(\varepsilon\) and function \(a(x)\). Numerical simulations of system show that the system exhibits different patterns of behavior and they significantly differ from those in a homogeneous medium.

MSC:
35K57 Reaction-diffusion equations
37N25 Dynamical systems in biology
47N20 Applications of operator theory to differential and integral equations
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